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4. The prime factorization forms of two numbers are 2¹ x 35 x 5³ x 7² a and 23 x 36 x 5 x 78.

a) Find the HCF of these two numbers in prime factorization form

b) Find the LCM of these two numbers in prime factorization form

please help me ;)

4 The Prime Factorization Forms Of Two Numbers Are 2 X 35 X 5 X 7 A And 23 X 36 X 5 X 78 A Find The HCF Of These Two Numbers In Prime Factorization Form B Find class=

Sagot :

Starrysoul100

[tex]\bold{\sf{\boxed{\huge{\blue{\underline{Solution 1}}}}}}[/tex]

[tex]\sf{ we\:have\:to\:find\:the\:HCF\:of\:the \:two\:given \:numbers}[/tex]

[tex]\bold{\underline{ Let's\: begin }}[/tex]

[tex]\sf{2¹ × 35 × 5³ × 7² ...(1) }[/tex]

[tex]\sf{23 × 36 × 5 × 78. ...(2)}[/tex]

[tex]\bold{\underline{ write\: ( 1) \:and\: (2) \: simultaneously }}[/tex]

[tex]\sf{ 2 × 5 × 7 ×5 × 5 × 5 × 7 × 7}[/tex]

[tex]\sf{ 23 × 6 × 6 × 5 × 2 * 13 * 3 }[/tex]

[tex]\bold{Thus, \:we\: got\: two\: common \:factor\: that\: is \:2 \:and \:5 }[/tex]

[tex]\sf{\underline{Therefore}}[/tex]

[tex]\sf{ 2 * 5 = 10}[/tex]

[tex]\bold{\pink{Hence \:,\: HCF \:of\:the\: given\: number \:is \:10}}[/tex]

[tex]\bold{\boxed{\huge{\blue{\underline{Solution 2}}}}}[/tex]

[tex]\sf{ we\:have\:to\:find\:the\:LCM\:of\:the \:two\:given \:numbers}[/tex]

[tex]\bold{\underline{ Let's\: begin }}[/tex]

[tex]\sf{2¹ × 35 × 5³ × 7² ...(1) }[/tex]

[tex]\sf{23 × 36 × 5 × 78. ...(2)}[/tex]

[tex]\bold{\underline{ write\: ( 1) \:and\: (2) \: simultaneously }}[/tex]

[tex]\sf{ 2 × 5 × 7 ×5 × 5 × 5 × 7 × 7}[/tex]

[tex]\sf{ 23 × 6 × 6 × 5 × 2 × 13 × 3 }[/tex]

[tex]\bold{Thus, \:we\: got\: two\: common \:factor\: that\: is \:2 \:and \:5 }[/tex]

[tex]\sf{\underline{Therefore}}[/tex]

[tex]\sf{ 2 × 5 × 7 × 5 × 5 × 5 × 7 × 7 × 23 × 6 × 6 × 13 × 3 }[/tex]

[tex]\bold{\pink{Hence \:,\: LCM \:of\:the\: given\: number \: = 9230130000}}[/tex]

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